I can't seem to get this to work no matter what.
And I know my way around the OS, security and networking.
Just where to look (don't tell me to read the source, please).
It would be nice to understand your frame of reference. The short answer is:
There does happen to be a bug with one or more of the v0.13 GUIs where
monerod does not automatically start up on its own. In that case, your wallet would have nothing to connect to. If you are in the settings and have 'local node' selected in the 'Node' tab, and you go to the 'Log' tab and type
status and it tells you it cannot connect to 127.0.0.1, then you'll need to manually start
monerod. So, in the same place you extracted everything else will be
monerod, so double-click it. Then you should be able to type
status in the GUI to confirm that it is downloading the blockchain.
Once the blockchain is downloaded (you can compare to moneroblocks.info or xmrchain.net, among others), you'll be able to use the wallet.
You should read the monero gui guide from erciccione here.
It does contain anything you should know from setting up the gui wallet to transactions.